Can you claim head of household if you are single but your boyfriend is living with you in your home and is unemployed showing no income?

No, and don't do it as the IRS will just bounce back your return.

You need to qualify the BF fisrt. Is he a citizen of the US and has a SSN? Has he lived with you the entire year? You said he shows no income - did he have ANY income more than $3,500 for the year? Did you pay for the household expenses alone? If yes, then you may file Single with one dependent.

Agreed!